Discrete-time performance analysis of a congestion control mechanism based on RED under multi-class bursty and correlated traffic
Introduction
With the rapid development of the Internet, the control of congestion has become one of the most critical issues in present networks to accommodate the increasingly diverse range of services and types of traffic that must be confronted by the users. It is also a major challenge to the researchers in the field of performance modelling. Congestion control to enable different types of Internet traffic to satisfy specified Quality of Service (QoS) constraints is becoming significantly important. Many systems in network environments require the queue to be monitored for impending congestion so that they can react anticipatively (Li et al., 1998).
Drop tail is a traditional technique used in congestion control at routers. It sets a maximum length for each queue at the router and accepts packets until the maximum queue length is reached. Once the queue length reaches the maximum limit, it drops packets until queue length is again below the maximum set value. This method has been used for several years in the Internet, but it has two important drawbacks: ‘Lock-Out’ and ‘Full Queues’ (Braden, 1998). First of all it is not suited to interactive network applications (such as voice–video session and web transfers requiring low end-to-end delay and jitter) because the drop-tail queue are always full or close to full for long periods of time and packets are continuously dropped when the queue reaches its maximum length. In return, delay will be large which will make interactive applications untenable. A second major disadvantage of drop tail is the global synchronization problem, which arises because the full queue length is unable to absorb bursty packet arrivals and thus many of them are dropped.
In order to overcome both problems and at the same time to provide low end-to-end delay along with high throughput, an approach called “active queue management” (AQM) has been proposed in the literature (Braden, 1998). This technique maintains a small size steady state queue which results in reduced packet loss, decreased end-to-end delay and the avoidance of lock-out behavior thus using the network resources more efficiently. Also, by keeping the average queue size small results in the efficient use of bandwidth and thus increases the link utilization by avoiding global synchronization. Furthermore, due to the availability of extra queue space, packet bursts will be absorbed as well. Finally, the bias of routers against flows that use small bandwidth due to monopolization of flows will be prevented, which will result in prevention of lock-out behavior.
A number of mechanisms have been proposed in the literature to implement AQM. These include random early detection (RED) (Floyd and Jacobson, 1993), random early marking (REM) (Lapsley and Low, 1999, Athuraliya et al., 2000), a virtual queue based scheme where the virtual queue is adaptive (Gibbens and Kelly, 1999, Kunniyur and Srikant, 2000, Kunniyur and Srikant, 2001) and a proportional integral controller mechanism (Hoolot et al., 2000), among others. Of the above schemes to implement AQM, the RED mechanism is the one recommended by The Internet Society in Braden (1998): Quote: “Unless a developer has reasons to provide another equivalent mechanism we recommend that RED be used”. This mechanism has the potential to overcome some of the problems discovered in drop-tail mechanisms which are specific to the Internet traffic, such as synchronization of TCP flows and correlation of the drop events (multiple packets dropped in sequence) within a TCP flow and it is therefore this mechanism that we will focus on in this paper.
In contrast to drop tail, RED (Floyd and Jacobson, 1993) drops arriving packets probabilistically depending on threshold settings in the queue. When the average queue length is less than a minimum threshold, all incoming packets are allowed to enter the queue. If the mean queue length is greater than a maximum threshold, every arriving packet is dropped. Between the minimum and maximum thresholds, incoming packets are dropped with a probability that increases linearly as a function of the mean queue length, reaching a maximum dropping probability at the maximum threshold.
Since the proposal of RED by Floyd and Jacobson (1993), most researchers have used simulation tools as the choice of modelling to examine the performance of various aspects of the RED mechanism. Only a few publications, such as Alazemi et al., 2000, May et al., 2000, Mokhtar and Azizoglu, 1999, Alazemi et al., 2001, have attempted to theoretically evaluate the performance of RED. To the authors’ knowledge, there is no clear description of the parameter settings and exact information being measured and it is very important and necessary to use an analytical approach to address the more fundamental aspects of the RED mechanism. This paper proposes a new analytical framework for the RED mechanism that takes into account the reduction in incoming multiple-class traffic arrival rate due to packets dropped probabilistically with the drop probability increasing linearly with system contents. More specifically, this paper presents a discrete-time finite capacity queue in the case of two traffic classes using MMBP-2 traffic arrival process for the performance evaluation of congestion control based on the RED mechanism using queue thresholds which incorporates a two-dimensional discrete-time Markov chain (each dimension corresponds to a traffic class with its own RED parameters) which captures the feedback effect of dropping packets on the incoming traffic. The stochastic analysis of the queue considered could be of interest for the performance evaluation of the RED mechanism for multi-class traffic with short range dependent (SRD) traffic characteristics. The discrete-time analysis would lend itself to high-speed networks that use slotted protocols, such as ATM.
The rest of the paper is organized as follows: The arrival process is introduced in Section 2. The discrete-time system model with two traffic classes is described in Section 3 including performance parameter measurements. The performance evaluation of the proposed model is presented through typical numerical experiments in Section 4. Finally, the conclusions and suggestion for future work follow in Section 5.
Section snippets
MMBP-2: the source model
Nowadays, for high-speed networks, correlation and burstiness are very important factors for system performance and thus a smooth Bernoulli process is no longer a good assumption for an arrival process of the network traffic in a discrete-time system. As queueing system performance is highly sensitive to correlation and bursty characteristics in the arrival process, the Markov-Modulated Bernoulli Process (MMBP) is widely used as a source model in the performance evaluation of high-speed network
Performance analysis of the proposed system
This section presents the description of the proposed model and analytical expressions for various performance metrics.
Numerical results
This section presents typical numerical results to demonstrate the credibility of the proposed analytical solution subject to various parameters settings. These results focus on evaluation of the aggregate system performance in terms of mean queue length (MQL), throughput, delay and packet loss probability; comparison analysis of marginal delay and loss probability between two traffic classes and the effects of traffic burstiness and the impact of traffic correlation upon various performance
Conclusions and future work
This paper presents a stochastic analysis of a discrete-time queue with multi-class bursty and correlated external traffic as an effective performance evaluation tool for Internet traffic congestion control. The analysis is based on the RED mechanism with two thresholds for each traffic class. The arrival process is based on the theory of two-dimensional discrete-time Markov chains to model two traffic classes by using an MMBP-2 arrival process (each dimension corresponds to a traffic class
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